多素数改良RSA算法的综合研究

Comprehensive Study on the Modified Multi-prime RSA Algorithm

为了进一步提升传统RSA算法的综合性能,在深入了解算法原理之后,将传统RSA算法转换为多素数改良RSA算法,在此基础上设计了3种优化方案.首先参数替换优化方法在密钥生成阶段引入了一个变量代替模数n,避免了对密钥的直接攻击.其次共享密钥优化方法在加密和解密阶段新增秘密密钥来提升运算复杂度,增加了破解难度,然后混合安全密钥优化方法则是在公钥和私钥的计算中加入许多中间因素,这使得计算更复杂,提升了安全性,最后对3种算法的性能进行了分析比较,结果表明混合安全密钥优化算法在安全性方面更胜一筹.

In order to further improve the comprehensive performance of the traditional RSA algorithm, after deep understanding of the algorithm principle, the traditional RSA algorithm is transformed into a modified multi-prime RSA algorithm. Based on this, three optimized schemes are designed as follows. Firstly, the parameter replacement optimization method introduces a variable surrogate modulus n in the key generation phase, which avoids direct attack on the key. Secondly, the shared key optimization method adds a secret key in the encryption and decryption phase to improve the computational complexity and increase the difficulty of cracking. Then, the hybrid security key optimization method adds many intermediate factors to the calculation of the public key and the private key, which makes the calculation more complicated and improves the security. Finally, the performance of the three algorithms is analyzed and compared. The results show that the hybrid security key optimization algorithm is superior in security.